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Let f(x) = ln x. (a) Construct the Lagrange polynomial for f passing through the points (1, In 1), (2, ln 2), and (3, ln 3). (b) Using the answer in part (a), approximate the values In(1.5) and In(2.4) and report the relative errors.

Let f(x) = ln x. (a) Construct the Lagrange polynomial for f passing through the points (1, In 1), (2, ln 2), and (3, ln 3). (b) Using the answer in part (a), approximate the values In(1.5) and In(2.4) and report the relative errors.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Let \( f(x) = \ln x \). (a) Construct the Lagrange polynomial for \( f \) passing through the points \((1, \ln 1)\), \((2, \ln 2)\), and \((3, \ln 3)\). (b) Using the answer in part (a), approximate the values \(\ln(1.5)\) and \(\ln(2.4)\) and report the relative errors.
Transcribed Image Text:**Problem Statement:** Let \( f(x) = \ln x \). (a) Construct the Lagrange polynomial for \( f \) passing through the points \((1, \ln 1)\), \((2, \ln 2)\), and \((3, \ln 3)\). (b) Using the answer in part (a), approximate the values \(\ln(1.5)\) and \(\ln(2.4)\) and report the relative errors.
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